Master Equation - Based Numerical Simulation in a Single Electron ...

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Numerical Simulations of Physical and Engineering Processes
Change of charge in capacitor is = − . Consider the equation (6b)
becomes,
= − ,
= ,
= e
(14)
Change of charge in capacitor is = − . Consider the equation (6c)
becomes,
= − − − ,
=− ,
=− e
(15)
2. Work done when one electron tunnel through capacitor ( ⟶ +)
Work done by power supply is a sum of multiplication between charge change in each
terminal and a given power supply voltage. Thus, when one electron tunnel through the
capacitor , the work becomes,
( ) = (+ ) +( ) + ( ) ×0,
( ) = +
−
The same calculation can be done when the single electron tunnel through the capacitor ,
as shown in Figure 3.
Fig. 3. The charge flow in the single electron transistor circuit when an electron tunnels
through the capacitor . 1. Change in charge when an electron through the capacitor ( ⟶ +)
Change of potential in the dot due to electron tunneling ( ⟶− or ⟶−1) is
= − , thus :
(16)